BUG: comparing strings of different dtypes errors

[a-reich]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd, numpy as np
arr1 = pd.array([],pd.StringDtype("pyarrow", na_value=pd.NA))
arr2 = pd.array([], pd.StringDtype("python", na_value=np.nan))
arr1 == arr2 # NotImplementedError: eq not implemented for <class 'pandas.core.arrays.string_.StringArrayNumpySemantics'>

Issue Description

This appears to be the type of issue discussed in #60639. That issue was closed, but I got an error when I tried running the above reproducer on the example given in the whatsnew for release 2.3.

My understanding was that the issue was closed when #61138 was merged to main, but it's unclear if the fix was successfully backported to the 2.3.x branch. I haven't had the time yet to try when building pandas myself from main.

Expected Behavior

Comparisons of string arrays/series with different dtypes should not error and the return dtype should follow the behavior laid out in #60639 .

Installed Versions

INSTALLED VERSIONS

commit : 2cc3762
python : 3.12.2
python-bits : 64
OS : Linux
OS-release : 6.6.87.1-microsoft-standard-WSL2
Version : #1 SMP PREEMPT_DYNAMIC Mon Apr 21 17:08:54 UTC 2025
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : C.UTF-8
LOCALE : C.UTF-8

pandas : 2.3.0
numpy : 2.2.6
pytz : 2025.2
dateutil : 2.9.0.post0
pip : None
Cython : None
sphinx : None
IPython : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : None
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
html5lib : None
hypothesis : None
gcsfs : None
jinja2 : None
lxml.etree : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 20.0.0
pyreadstat : None
pytest : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlsxwriter : None
zstandard : None
tzdata : 2025.2
qtpy : None
pyqt5 : None